MASTER ADVANCED PHYSICS
(FOR ALL TOP EXAMS)
VECTORS – 2
Few Basic Concepts in Vector Algebra
We have seen that a vector is inherently a quantity that has both magnitude and direction. We cannot add vectors like normal addition. We need to consider both magnitude and direction and find ways to get the final effect or what is called a resultant.
Before we go into that, let us understand a few basic concepts that are needed to find resultants.
Negative vector –
A negative vector is simply the same vector with the same magnitude but exactly the opposite direction.
Like and unlike vectors –
Like vectors are those that may differ in magnitude but have the same direction.
Unlike vectors have different magnitude but have directions exactly opposite to each other.
Equality of vectors –
If two vectors have BOTH same magnitude and the same direction, they are called equal vectors.
Unit vector –
A vector having unit magnitude, means one, but the same direction as a given vector, is called UNIT VECTOR of the given vector.
So, we if we have a vector of 5 units and a direction of 60 degrees from horizontal, then the unit vector is simply ONE unit at 60 degrees from horizontal.
It is convenient to have 3 unit vectors in 3 directions, x, y, and z as shown.
Then we have a special symbol ,
I cap, j cap, k cap for unit vectors along x, y, and z axes respectively.
Multiplication of a vector by a real number -
We simply multiply the real number with the magnitude of the vector and the direction remains the same.
For example, if we have a vector with 5 units magnitude and 60 degrees from the horizontal as direction. Multiplication of 3 with the number is simply
3 multiplied by 5. So, we have 15 units of magnitude and the same 60 degrees direction.